The American black bear (Ursus americanus) is one of eight bear species in the world. It is thesmallest North American bear and the most common bear specieson the planet. In 1969, Dr. Michael R. Pelton of the University ofTennessee initiated a long-term study of the population in the GreatSmoky Mountains National Park. One aspect of the study was todevelop a model that could be used to predict a bear's weight (sinceit is not practical to weigh bears in the field). One variable thoughtto be related to weight is the length of the bear. The following datarepresent the lengths and weights of 12 American black bears.

(a) Test whether a linear relation exists between total length and weight at the = 0.05 level of significance.

Step 1: Parameter of interest:

H:1 versusH1:10

Step 2: Test statistic: ( Useb1=1.6942)

sb1= (Round to four decimal places)

t= (Round your test statistic to four decimal places)

Step 3: Classical approach

= ,t2= (Rounded to three decimal places)

Does the test statistic lie in the rejection region? (yes, no)

Step 3: p-value approach

p-value= (Rounded to four decimal places)

What is the relationship between p-value and? p-value . (>, <)

Step 5: Conclusion:

Is there sufficient evidence to support the alternative hypothesis? (yes, no)

(b)Construct a 95% confidence interval for the slope of the true regression line,1.

Use. and round your answer to four decimal places.

Answer: ( , )